Subjective Rationalizability in Hypergames

A new solution concept for hypergames called subjective rationalizability is proposed. Hypergame theory is a game theoretical framework that deals with agents who may misperceive game structures and explicitly takes into account hierarchy of perceptions, that is, an agent’s view about another agent’s view and so on. An action of an agent is called subjectively rationalizable when the agent thinks it can be a best response to the other’s choices, each of which the agent thinks each agent thinks is a best response to the other’s choices, and so on. Then it is proved that subjective rationalizability is equivalent to the standard notion of rationalizability under a condition called inside common knowledge. The result makes the new solution concept a practical tool in hypergame analyses. Theoretically, it is characterized as such a concept that provides the precise implication, that is, predicted outcomes, of a given hypergame structure. 1. Introduction Hypergame theory deals with misperceptions of agents (decision makers) in games by relaxing common knowledge often assumed in the standard game theory [1, 2]. It is the basic idea of hypergames that each agent is supposed to possess independently a subjective view about a game called her subjective game and make a decision based on it. The idea allows agents to hold different perceptions and thus enables us to capture realistic aspects of many interactive decision making situations given that misperceptions are everyday affairs in our life. In game theory, Bayesian games are often referred to as the standard model to deal with incomplete information [3]. While a hypergame can technically be reformulated as a Bayesian game under specific conditions, the reformulation requires the agents to be aware of every possibility indeed relevant to the situation [4]. Therefore hypergames are unique in that they can directly deal with unawareness of agents. Although hypergame theory has been developed in several ways, the framework the present study deals with explicitly takes into account hierarchy of perceptions, that is, an agent’s view about another agent’s view and so on [5–8]. It can describe not only situations in which an agent may perceive a game differently from the others but also situations in which she may notice that other agents may perceive the game differently, and moreover the other agents may also notice that the other agents may see different games and so on. Such a hierarchy of perceptions is formalized by using the concept of viewpoint. For example, agent ’s view about agent ’s view about agent ’s